Interpret the key results for Display Descriptive Statistics

Complete the following steps to interpret display descriptive statistics. Key output includes N, the mean, the median, the standard deviation, and several graphs.

Step 1: Describe the size of your sample

Use N to know how many observations are in your sample. Minitab does not include missing values in this count.

You should collect a medium to large sample of data. Samples that have at least 20 observations are often adequate to represent the distribution of your data. However, to better represent the distribution with a histogram, some practitioners recommend that you have at least 50 observations. Larger samples also provide more precise estimates of the process parameters, such as the mean and standard deviation.

Descriptive Statistics: Torque

Statistics Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Torque 68 0 21.265 0.779 6.422 10.000 16.000 20.000 24.750 Variable Maximum Torque 37.000
Key Result: N

In these results, you have 68 observations.

Step 2: Describe the center of your data

Use the mean to describe the sample with a single value that represents the center of the data. Many statistical analyses use the mean as a standard measure of the center of the distribution of the data.

The median is another measure of the center of the distribution of the data. The median is usually less influenced by outliers than the mean. Half the data values are greater than the median value, and half the data values are less than the median value.

The median and the mean both measure central tendency. But unusual values, called outliers, can affect the median less than they affect the mean. If your data are symmetric, the mean and median are similar.
Symmetric
Not symmetric

For the symmetric distribution, the mean (blue line) and median (orange line) are so similar that you can't easily see both lines. But the non-symmetric distribution is skewed to the right.

Descriptive Statistics: Torque

Statistics Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Torque 68 0 21.265 0.779 6.422 10.000 16.000 20.000 24.750 Variable Maximum Torque 37.000
Key Results: Mean and Median

In these results, the mean torque that is required to remove a toothpaste cap is 21.265, and the median torque is 20. The data appear to be skewed to the right, which explains why the mean is greater than the median.

Step 3: Describe the spread of your data

Use the standard deviation to determine how spread out the data are from the mean. A higher standard deviation value indicates greater spread in the data.

Descriptive Statistics: Torque

Statistics Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Torque 68 0 21.265 0.779 6.422 10.000 16.000 20.000 24.750 Variable Maximum Torque 37.000
Key Result: StDev

In these results, the standard deviation is 6.422. With normal data, most of the observations are spread within 3 standard deviations on each side of the mean.

Step 4: Assess the shape and spread of your data distribution

Use the histogram, the individual value plot, and the boxplot to assess the shape and spread of the data, and to identify any potential outliers.

Examine the spread of your data to determine whether your data appear to be skewed

When data are skewed, the majority of the data are located on the high or low side of the graph. Often, skewness is easiest to detect with a histogram or boxplot.

Right-skewed
Left-skewed

The histogram with right-skewed data shows wait times. Most of the wait times are relatively short, and only a few wait times are long. The histogram with left-skewed data shows failure time data. A few items fail immediately, and many more items fail later.

Determine how much your data varies

Assess the spread of the points to determine how much your sample varies. The greater the variation in the sample, the more the points will be spread out from the center of the data.

This individual value plot shows that the data on the right has more variation than the data on the left.

Look for multi-modal data

Multi-modal data have multiple peaks, also called modes. Multi-modal data often indicate that important variables are not yet accounted for.

If you have additional information that allows you to classify the observations into groups, you can create a group variable with this information. Then, you can create the graph with groups to determine whether the group variable accounts for the peaks in the data.

Simple
With Groups

For example, a manager at a bank collects wait time data and creates a simple histogram. The histogram appears to have two peaks. After further investigation, the manager determines that the wait times for customers who are cashing checks is shorter than the wait time for customers who are applying for home equity loans. The manager adds a group variable for customer task, and then creates a histogram with groups.

Identify outliers

Outliers, which are data values that are far away from other data values, can strongly affect the results of your analysis. Often, outliers are easiest to identify on a boxplot.

On a boxplot, asterisks (*) denote outliers.

Try to identify the cause of any outliers. Correct any data–entry errors or measurement errors. Consider removing data values for abnormal, one-time events (also called special causes). Then, repeat the analysis. For more information, go to Identifying outliers.

Step 5. Compare data from different groups

If you have a By variable that identifies groups in your data, you can use it to analyze your data by group or by group level.

Descriptive Statistics: Torque

Statistics Variable Machine N N* Mean SE Mean StDev Minimum Q1 Median Torque 1 36 0 18.667 0.732 4.395 10.000 15.250 17.000 2 32 0 24.19 1.26 7.12 14.00 17.50 24.00 Variable Machine Q3 Maximum Torque 1 21.750 30.000 2 31.00 37.00

In these results, the summary statistics are calculated separately by machine. You can easily see the differences in the center and spread of the data for each machine. For example, Machine 1 has a lower mean torque and less variation than Machine 2. To determine whether the difference in means is significant, you can perform a 2-sample t-test.

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